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Problem 42


Problem 42


Coded triangle numbers

The nth term of the sequence of triangle numbers is given by, tn = 1/2n(n+1); so the first ten triangle numbers are:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle number then we shall call the word a triangle word.

Using words.txt(right click and ‘Save Link/Target As…’), a 16K text file containing nearly two-thousand common English words, how many are triangle words?


编码三角形数

三角形数序列的第n项由公式tn = 1/2n(n+1)给出;因此前十个三角形数是:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

将一个单词的每个字母分别转化为其在字母表中的顺序并相加,我们可以计算出一个单词的值。例如,单词SKY的值就是 19 + 11 + 25 = 55 = t10。如果一个单词的值是一个三角形数,我们就称这个单词为三角形单词。

在这个16K的文本文件words.txt (右击并选择“目标另存为……”)中包含有将近两千个常用英文单词,这其中有多少个三角形单词?